Constrained Probabilistic Mask Learning for Task-specific Undersampled MRI Reconstruction

Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling patterns following various strategies, e.g., variable density sampling or radial trajectories. In this work, we propose a method that directly learns the undersampling masks from data points, thereby also providing task- and domain-specific patterns. To solve the resulting discrete optimization problem, we propose a general optimization routine called ProM: A fully probabilistic, differentiable, versatile, and model-free framework for mask optimization that enforces acceleration factors through a convex constraint. Analyzing knee, brain, and cardiac MRI datasets with our method, we discover that different anatomic regions reveal distinct optimal undersampling masks, demonstrating the benefits of using custom masks, tailored for a downstream task. For example, ProM can create undersampling masks that maximize performance in downstream tasks like segmentation with networks trained on fully-sampled MRIs. Even with extreme acceleration factors, ProM yields reasonable performance while being more versatile than existing methods, paving the way for data-driven all-purpose mask generation.